Can you use experiments to explain Archimedes method and basis for finding out the crown mystery 10

First of all, we must measure the mass m and volume v of the alloy, find m with a balance or a scale with high precision, it may be more troublesome to measure v, depending on its shape, if it is a regular geometry, you can use a ruler to measure, and then use a formula to calculate; If not, the drainage method can be used, i.e., v=v drainage. The alloy density is then calculated from p(rou)=m v (for convenience, it is denoted by t later).

The next step is to train the system of equations.

Let the densities of the metals A and B that make up the alloy be E and F respectively (this should be known), and let the masses of metals A and B be Ma and MB, then there is:

Equation 1: mA+mb=m

Equation 2: m (ma e + mb f) = t

Simultaneous solution, the masses of the two metals can be obtained.

Archimedes checked"Crown Mystery Case"Using the physical method described above, he submerged the crown in water, divided the mass of the crown by the volume of water it displaced, and found that the density of the crown was less than that of gold, so it must be adulterated.

King Aherro of Sygura gave the goldsmith a piece of ** and asked him to make a crown. After the crown was made, the king felt a little light in his hand. He suspected that the goldsmith had adulterated it, but the goldsmith vouched for it with his head and weighed it in front of him, and the result was as heavy as the original nugget.

The king was still suspicious, but he could not produce any evidence, so he called Archimedes and asked him to solve the problem.

After returning home, Archimedes closed his door and pondered, but he was puzzled.

One day, his wife forced him to take a bath. When he jumped into the pool, the water overflowed from the pool. Archimedes heard the sound of running water, and inspiration struck him.

He jumped out of the pool, without even putting on his clothes, and rushed out into the street, shouting:"Youlega! Youlega!

Meaning discovered)."。Madame was really anxious this time, and muttered"It's crazy, it's crazy", and then chased him out. The people on the street didn't know what was going on, and they all followed after them.

It turned out that Archimedes had found a solution to the crown problem by overflowing the bathtub: the same substance of the same mass was soaked in water, and the volume of the overflowing water should be the same. If the crown is placed in the water, the volume of the overflowing water should be the same as that of a gold nugget of the same mass, otherwise the crown must be adulterated.

Akiweide ran to the palace and immediately found a basin of water, and found a piece of **, a piece of ** of the same weight, and soaked it in the basin twice, **overflowing water was almost twice as much as **overflowing, and then he soaked the crown and the gold nugget into the basin respectively, and the crown overflowed more water than the gold nuggets, obviously the mass of the crown is not equal to the mass of the gold nuggets, and the crown must have been adulterated. In the face of the iron facts, the goldsmith had to bow his head and admit that the crown was indeed mixed with **. The mystery of the annoying crown has finally been solved.

He first measured the weight of the crown, and then prepared a nugget of pure gold and a nugget of pure silver, which weighed as much as the crown, and a container filled with water. Archimedes slowly sank the nuggets of pure gold into the container and counted the amount of water that had overflowed, and according to his reasoning, the volume of the water was the volume of the nuggets of pure gold. Archimedes then sank the silver nuggets into a container filled with water, and calculated the volume of the silver nuggets based on the amount of water that had spilled.

Of course, silver nuggets are larger than gold nuggets. Finally, he placed the crown in a container filled with water and measured the volume of the crown based on the amount of water that had overflowed. Archimedes compared the volume of the crown with that of pure gold and silver, and found that the crown was larger than the volume of pure gold and smaller than that of pure silver, which proves that the crown was not made of pure gold, but of a mixture of gold and silver.

According to the measured results, he also calculated how many ** were replaced with**, and finally solved the mystery of the crown. He told the goldsmith about his test, and the goldsmith had to admit his guilt.

King Chailaku asked a craftsman to make a crown of pure gold. The king would come to him and ask him to determine whether the crown was adulterated without damaging it.

That's a problem. Archimedes went home and meditated for a few days, but he couldn't eat or sleep. One day, while he was taking a bath, he found that when his body sank in the tub, some of the water overflowed from the side of the tub; Moreover, he felt that the deeper he entered the water, the less weight he weighed.

Got it! Got it! A way to weigh the crown has been found!

He jumped out of the tub and shouted in joy.

Archimedes immediately entered the palace and placed a piece of gold, a piece of silver, and a crown in a basin of water, which weighed as much as the crown, and saw that the amount of water discharged by the nuggets of gold was less than that of the nuggets of silver, and the amount of water that the crown put out was more than the amount of water that was discharged by the nuggets of gold. Archimedes confidently said to the king, "The crown is mixed with silver!"

The king didn't understand it, and asked Archimedes to explain. Archimedes, said: A kilogram of wood is larger than a kilogram of iron.

If they are put into the water separately, the large wood will discharge more water than the smaller iron will put out more water. I apply this to gold, silver, and crowns. Because the density of gold is high and the density of silver is small, therefore, the volume of silver and silver of the same weight must be greater than the volume of gold, and when put into water, the amount of water discharged by the gold nugget is less than that of the silver bar.

In the experiment just now, the crown emits more water than gold, indicating that the density of the crown is less than that of the gold nuggets, thus proving that the crown is not made of pure gold. 」

The king was convinced. It turns out that the craftsman embezzled **.

When you think of taking a bath, put the crown in a container full of water, and the volume of water that overflows is the crown volume.

He put gold of the same quality as the crown into the water, and compared the overflowing water with the water that overflowed when he put the crown into the water, and if it was different, the crown was adulterated. Since they are all the same thing, the same quality, then whoever overflows should be the same anyway.

Archimedes found a piece of **, a piece of ** of the same weight, and soaked it in the basin twice, and the water that overflowed was almost twice as much as the water that overflowed, and then he soaked the crown and the gold nugget into the basin separately, and the crown overflowed more water than the gold nuggets, and it was obvious that the mass of the crown was not equal to the mass of the gold nuggets, and the crown must have been adulterated.

Five under the science book on it.

Hello! It is the density of the substance that is utilized.

The volume of the crown is measured by the drainage method (because the shape of the crown is irregular), and the weight of the crown is calculated according to the density value of **.

Is this it?

The king asked a craftsman to forge a golden crown for him. The king gave the craftsman the amount of ** he needed. The craftsmanship of the craftsmen is very high, and the crown made is exquisite and unique, and the weight is as heavy as the ** given by the king at the beginning.

However, it was reported to the king: "When the craftsmen made the crown, they secretly swallowed up a part of the ** and mixed it with the same weight of silver." When the king heard this, he also became suspicious, so he called Archimedes and asked him to determine whether the gold crown was mixed with silver and whether the craftsman had embezzled it.

This time, Archimedes was stumped. He went home and thought about it for a long time, but he didn't come up with a way, he couldn't eat every day, he couldn't sleep well, and he didn't take a bath, as if he was enchanted.

One day, the king sent someone to urge him to report to the palace. His wife saw that he was too dirty and forced him to take a bath. While he was taking a bath in the bathhouse, he was still thinking about the problem of weighing the crown.

Suddenly, he noticed that when his body sank in the tub, some of the water was spilling out of the side of the tub. At the same time, he felt that the deeper he entered the water, the lighter his body became. So, he immediately jumped out of the tub, forgot to put on his clothes, and ran out into the street where the crowd was.

While running, he shouted: "I've come up with it, I've come up with it, I've found a way to solve the crown!" ”

When he entered the palace, he said to the king, "Allow me to do an experiment before I can report the results to you." The king agreed.

Archimedes placed a piece of gold, a piece of silver, and a crown as heavy as a crown in a basin of water, and saw that the amount of water discharged by the gold nugget was less than that of the silver bar, and the amount of water discharged by the crown was more than that of the gold nugget.

Archimedes said to the king: "The crown is mixed with silver!" The king looked at the experiment, but did not understand it, and asked Archimedes to explain it.

Archimedes, said: A kilogram of wood is larger than a kilogram of iron. If they are put into the water separately, the larger wood will discharge more water than the smaller iron.

I apply this to gold, silver, and crowns. Because gold is denser and silver is less dense, gold and silver, which weigh the same weight, must be greater than the volume of gold. Therefore, if the same weight of gold and silver is put into the water, then the amount of water discharged by the gold bar is less than that of the silver bar.

The experiment just showed that the crown emits more water than the gold nuggets, indicating that the density of the crown is less than that of the gold nuggets, which proves that the crown is not made of pure gold. Archimedes' coherent narration convinced the king. The results of the experiment proved that the craftsman had swallowed **.

The king made a golden crown for the merchant Jinrang. When he had done this, the king thought that the merchant had done something, but the weight of the crown was the same as the weight of the gold he had been given. The king asked Archimedes to find a way to argue the question of the gold content of the crown.

Archimedes later came up with a solution, based on the current principle of density of matter, that is, the weight of gold per unit volume is a quantifier. Legend has it that he discovered this natural law while taking a bath, and left behind a famous saying: Eureka (I found out).